Q4 of 23 Page 187

In the adjacent figure ABCD is a parallelogram P, Q are the midpoints of sides AB and DC respectively. Show that PBCQ is also a parallelogram.


Given:-ABCD is a parallelogram


P,Q are the midpoints of sides AB and DC respectively.


Solution:-


In parallelogram ABCD


If P,Q are the midpoints of sides AB and DC respectively


∴ DC=2QC=2QD


∴ AB=2AP=2PB


If DC||AB


Then;


QD||AP and QC||PB


Line PQ divides the parallelogram in 2 equal parts


Because P and Q are midpoints


∴ AD||PQ||CB


If;


PQ||CB and QC||PB


Then, PBCQ is also a parallelogram


More from this chapter

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Find the measure of all the angles of a parallelogram, if one angle is 24° less than the twice of the smallest angle.

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In the adjacent figure ABCD is a parallelogram and E is the midpoint of the side BC. If DE and AB are produced to meet at F, show that AF = 2AB.


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ABC is an isosceles triangle in which AB = AC. AD bisects exterior angle QAC and CD || BA as shown in the figure. Show that

(i) ∠DAC = ∠BCA


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ABCD is a parallelogram AP and CQ are perpendiculars drawn from vertices A and C on diagonal BD (see figure) show that

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